t-Test

The figure below shows the relationship between confidence intervals and the result of a t-test. (a) The shaded area under the normal distribution curve shows the confidence interval for the sample based on t_exp. Based on the sample, we expect μ to fall within the shaded area. The solid bars in (b) and (c) show the confidence intervals for μ explained by indeterminate error given the choice of α and the available degrees of freedom, n. For (b) we must reject the null hypothesis because there are portions of the sample’s confidence interval that lie outside the confidence interval due to indeterminate error. In the case of (c) we retain the null hypothesis because the confidence interval due to indeterminate error completely encompasses the sample’s confidence interval.